The SCUBA-2 Cosmology Legacy Survey: The EGS deep field -- III. The evolution of faint submillimeter galaxies at $z

We present a demographic analysis of the physical and morphological properties of $450/850~\mu\rm m$-selected galaxies from the deep observations of the SCUBA-2 Cosmology Legacy Survey in the Extended Groth Strip that are detected below the classical submillimeter-galaxy regime ($S_{850 \mu\rm m}\lesssim 6~\rm mJy$/beam) and compare them with a sample of optically-selected star-forming galaxies detected in the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey in the same field. We derive the evolution of the main sequence of star-forming galaxies, finding a steeper specific star formation rate versus stellar mass at $z>2.5$ than previous studies. Most faint submillimeter-galaxies fall within $3\sigma$ of the main sequence, but 40~per cent are classified as starbursts. Faint submillimeter galaxies have 50~per cent larger sizes at $2